RS Aggarwal Solutions: Bar Graph, Histogram and Frequency Polygon- 2 | Mathematics (Maths) Class 9 PDF Download

 Page 1


        
      
       
      
       
     
      
               
                
               
      
Q u e s t i o n : 1 3
The daily wages of 50 workers in a factory are given below:
Page 2


        
      
       
      
       
     
      
               
                
               
      
Q u e s t i o n : 1 3
The daily wages of 50 workers in a factory are given below:
Daily wages
in
340-380 380-420 420-460 460-500 500-540 540-580
Number of
workers
16 9 12 2 7 4
Construct a histogram to represent the above frequency distribution.
S o l u t i o n :
The given frequency distribution is in exclusive form.
We will represent the class intervals
dailywages(inrupees)
along the x-axis & the corresponding frequencies
numberofworkers
along the y-axis.
The scale is as follows:
On x-axis: 1 big division = 40 rupees
On y-axis: 1 big division = 2 workers
Because the scale on the x-axis starts at 340, a kink, i.e., a  break, is indicated near the origin to signify that the
graph is drawn with a scale beginning at 340
and not at the origin.
We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.
Thus, we will obtain the following histogram:
Q u e s t i o n : 1 4
The following table shows the average daily earnings of 40 general stores in a market, during a certain week.
Daily earning 
inrupees
700-750 750-800 800-850 850-900 900-950 950-1000
Number of
stores
6 9 2 7 11 5
Draw a histogram to represent the above data.
S o l u t i o n :
The given frequency distribution is in exclusive form.
We will represent the class intervals
dailyearnings(inrupees)
along the x-axis & the corresponding frequencies
numberofstores
Page 3


        
      
       
      
       
     
      
               
                
               
      
Q u e s t i o n : 1 3
The daily wages of 50 workers in a factory are given below:
Daily wages
in
340-380 380-420 420-460 460-500 500-540 540-580
Number of
workers
16 9 12 2 7 4
Construct a histogram to represent the above frequency distribution.
S o l u t i o n :
The given frequency distribution is in exclusive form.
We will represent the class intervals
dailywages(inrupees)
along the x-axis & the corresponding frequencies
numberofworkers
along the y-axis.
The scale is as follows:
On x-axis: 1 big division = 40 rupees
On y-axis: 1 big division = 2 workers
Because the scale on the x-axis starts at 340, a kink, i.e., a  break, is indicated near the origin to signify that the
graph is drawn with a scale beginning at 340
and not at the origin.
We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.
Thus, we will obtain the following histogram:
Q u e s t i o n : 1 4
The following table shows the average daily earnings of 40 general stores in a market, during a certain week.
Daily earning 
inrupees
700-750 750-800 800-850 850-900 900-950 950-1000
Number of
stores
6 9 2 7 11 5
Draw a histogram to represent the above data.
S o l u t i o n :
The given frequency distribution is in exclusive form.
We will represent the class intervals
dailyearnings(inrupees)
along the x-axis & the corresponding frequencies
numberofstores
numberofstores
along the y-axis.
The scale is as follows:
On x-axis: 1 big division = 50 rupees
On y-axis: 1 big division = 1 store
Because the scale on the x-axis starts at 700, a kink, i.e., a break is indicated near the origin to signify that the
graph is drawn with a scale beginning at 700 and not at the origin.
We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.
Thus, we will obtain the following histogram:
Q u e s t i o n : 1 5
The heights of 75 students in a school are given below:
Height incm 130-136 136-142 142-148 148-154 154-160 160-166
Number of students 9 12 18 23 10 3
Draw a histogram to represent the above data.
S o l u t i o n :
The given frequency distribution is in exclusive form.
We will represent the class intervals
heights(incm)
along the x-axis & the corresponding frequencies
numberofstudents
along the y-axis.
The scale is as follows:
On x-axis: 1 big division = 6 cm
On y-axis: 1 big division = 2 students
Because the scale on the x-axis starts at 130, a kink, i.e., a break, is indicated near the origin to signify that the
graph is drawn with a scale beginning at 130
and not at the origin.
We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.
Thus, we will obtain the following histogram:
Page 4


        
      
       
      
       
     
      
               
                
               
      
Q u e s t i o n : 1 3
The daily wages of 50 workers in a factory are given below:
Daily wages
in
340-380 380-420 420-460 460-500 500-540 540-580
Number of
workers
16 9 12 2 7 4
Construct a histogram to represent the above frequency distribution.
S o l u t i o n :
The given frequency distribution is in exclusive form.
We will represent the class intervals
dailywages(inrupees)
along the x-axis & the corresponding frequencies
numberofworkers
along the y-axis.
The scale is as follows:
On x-axis: 1 big division = 40 rupees
On y-axis: 1 big division = 2 workers
Because the scale on the x-axis starts at 340, a kink, i.e., a  break, is indicated near the origin to signify that the
graph is drawn with a scale beginning at 340
and not at the origin.
We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.
Thus, we will obtain the following histogram:
Q u e s t i o n : 1 4
The following table shows the average daily earnings of 40 general stores in a market, during a certain week.
Daily earning 
inrupees
700-750 750-800 800-850 850-900 900-950 950-1000
Number of
stores
6 9 2 7 11 5
Draw a histogram to represent the above data.
S o l u t i o n :
The given frequency distribution is in exclusive form.
We will represent the class intervals
dailyearnings(inrupees)
along the x-axis & the corresponding frequencies
numberofstores
numberofstores
along the y-axis.
The scale is as follows:
On x-axis: 1 big division = 50 rupees
On y-axis: 1 big division = 1 store
Because the scale on the x-axis starts at 700, a kink, i.e., a break is indicated near the origin to signify that the
graph is drawn with a scale beginning at 700 and not at the origin.
We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.
Thus, we will obtain the following histogram:
Q u e s t i o n : 1 5
The heights of 75 students in a school are given below:
Height incm 130-136 136-142 142-148 148-154 154-160 160-166
Number of students 9 12 18 23 10 3
Draw a histogram to represent the above data.
S o l u t i o n :
The given frequency distribution is in exclusive form.
We will represent the class intervals
heights(incm)
along the x-axis & the corresponding frequencies
numberofstudents
along the y-axis.
The scale is as follows:
On x-axis: 1 big division = 6 cm
On y-axis: 1 big division = 2 students
Because the scale on the x-axis starts at 130, a kink, i.e., a break, is indicated near the origin to signify that the
graph is drawn with a scale beginning at 130
and not at the origin.
We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.
Thus, we will obtain the following histogram:
Q u e s t i o n : 1 6
The following table gives the lifetimes of 400 neon lamps:
Lifetime
inhr
300-400 400-500 500-600 600-700 700-800 800-900 900-1000
Number
of
lamps
14 56 60 86 74 62 48
i
Represent the given information with the help of a histogram.
ii
How many lamps have a lifetime of more than 700 hours?
S o l u t i o n :
i
ii
Lamps with lifetime more than 700 hours = 74 + 62 + 48 = 184 
Q u e s t i o n : 1 7
Page 5


        
      
       
      
       
     
      
               
                
               
      
Q u e s t i o n : 1 3
The daily wages of 50 workers in a factory are given below:
Daily wages
in
340-380 380-420 420-460 460-500 500-540 540-580
Number of
workers
16 9 12 2 7 4
Construct a histogram to represent the above frequency distribution.
S o l u t i o n :
The given frequency distribution is in exclusive form.
We will represent the class intervals
dailywages(inrupees)
along the x-axis & the corresponding frequencies
numberofworkers
along the y-axis.
The scale is as follows:
On x-axis: 1 big division = 40 rupees
On y-axis: 1 big division = 2 workers
Because the scale on the x-axis starts at 340, a kink, i.e., a  break, is indicated near the origin to signify that the
graph is drawn with a scale beginning at 340
and not at the origin.
We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.
Thus, we will obtain the following histogram:
Q u e s t i o n : 1 4
The following table shows the average daily earnings of 40 general stores in a market, during a certain week.
Daily earning 
inrupees
700-750 750-800 800-850 850-900 900-950 950-1000
Number of
stores
6 9 2 7 11 5
Draw a histogram to represent the above data.
S o l u t i o n :
The given frequency distribution is in exclusive form.
We will represent the class intervals
dailyearnings(inrupees)
along the x-axis & the corresponding frequencies
numberofstores
numberofstores
along the y-axis.
The scale is as follows:
On x-axis: 1 big division = 50 rupees
On y-axis: 1 big division = 1 store
Because the scale on the x-axis starts at 700, a kink, i.e., a break is indicated near the origin to signify that the
graph is drawn with a scale beginning at 700 and not at the origin.
We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.
Thus, we will obtain the following histogram:
Q u e s t i o n : 1 5
The heights of 75 students in a school are given below:
Height incm 130-136 136-142 142-148 148-154 154-160 160-166
Number of students 9 12 18 23 10 3
Draw a histogram to represent the above data.
S o l u t i o n :
The given frequency distribution is in exclusive form.
We will represent the class intervals
heights(incm)
along the x-axis & the corresponding frequencies
numberofstudents
along the y-axis.
The scale is as follows:
On x-axis: 1 big division = 6 cm
On y-axis: 1 big division = 2 students
Because the scale on the x-axis starts at 130, a kink, i.e., a break, is indicated near the origin to signify that the
graph is drawn with a scale beginning at 130
and not at the origin.
We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.
Thus, we will obtain the following histogram:
Q u e s t i o n : 1 6
The following table gives the lifetimes of 400 neon lamps:
Lifetime
inhr
300-400 400-500 500-600 600-700 700-800 800-900 900-1000
Number
of
lamps
14 56 60 86 74 62 48
i
Represent the given information with the help of a histogram.
ii
How many lamps have a lifetime of more than 700 hours?
S o l u t i o n :
i
ii
Lamps with lifetime more than 700 hours = 74 + 62 + 48 = 184 
Q u e s t i o n : 1 7
Draw a histogram for the frequency distribution of the following data.
Class interval 8-13 13-18 18-23 23-28 28-33 33-38 38-43
Frequency 320 780 160 540 260 100 80
S o l u t i o n :
The given frequency distribution is in exclusive form.
We will represent the class intervals along the x-axis & the corresponding frequencies along the y-axis.
The scale is as follows:
On x-axis: 1 big division = 5 units
On y-axis: 1 big division = 50 units
Because the scale on the x-axis starts at 8, a kink, i.e., a break, is indicated near the origin to signify that the graph
is drawn with a scale beginning at 8
and not at the origin.
We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.
Thus, we will obtain the following histogram:
Q u e s t i o n : 1 8
Construct a histogram for the following frequency distribution.
Class interval 5-12 13-20 21-28 29-36 37-44 45-52
Frequency 6 15 24 18 4 9
S o l u t i o n :
The given frequency distribution is in inclusive form.
So, we will convert it into exclusive form, as shown below:
 
 Class
Interval
Frequency
4.5–12.5 6
12.5–20.5 15
20.5–28.5 24
28.5–36.5 18
36.5–44.5 4
44.5–52.5 9
We will mark class intervals along the x-axis and frequencies along the y-axis.
The scale is as follows:
On x-axis: 1 big division = 8 units